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Rendering particles into trails (slow-mo?)

However, in the comments, a user called Nerver Cheng did something that gave the particles a visible trail, and even the poster wasn't sure how it happened:

I tried replicating the effect, and couldn't figure it out. Motion Blur? Nope, motion blur interpolates in straight lines. These particles curve beautifully.
Deformation Blur (in Motion Blur panel under Object tab in Properties)? Nope, that should only affect the mesh, not the particles it emits.
Trails, halo materials etc? Cycles doesn't support trails, and the image seems to have fireflies and "pixelation" typical of Cycles rendering. Also,

So... what's going on?

I can't seem to find a rendering option or setup that would make particles look like this.

A theory: Perhaps this isn't caused by rendering, but by particle motion? Maybe this is caused by a single Turbulence field, where the field itself doesn't change between frames. The "trails" consist of thousands of particles, where each newly spawned particle follows the exact same path in the turbulence field, creating what looks like a trail. I tried doing this; it didn't work, but I just put Noise down to 0 and I'm not sure if that's enough to make the Turbulence field not animate.

Also, this was posted about 4 years ago, so it could even have been a bug that's been fixed long ago!

One possibility is that it is rendered in Blender Internal, and Sampled Motion Blur works this nicely with particles. However, someone was trying to use Blender Internal for this a few years ago, and wasn't able to do the same effect ( http://blender.stackexchange.com/que...ing-the-emitte ).